What is the value of the binary number 01101? A. 4 B. 13 C. 25 D. 29 E. 31
The Correct Answer and Explanation is :
The value of the binary number 01101 is 13 (Option B).
Explanation:
Binary numbers use a base-2 system, meaning each digit represents a power of 2, starting from the rightmost digit, which represents (2^0). Each digit in a binary number can either be a 0 or a 1. The position of each digit indicates its weight based on powers of 2.
To convert the binary number 01101 to its decimal (base-10) equivalent, we start from the rightmost digit and assign powers of 2 to each digit as follows:
- The rightmost digit (1) is at position 0: (0 \times 2^0 = 0)
- The next digit (0) is at position 1: (1 \times 2^1 = 2)
- The next digit (1) is at position 2: (1 \times 2^2 = 4)
- The next digit (1) is at position 3: (1 \times 2^3 = 8)
- The leftmost digit (0) is at position 4: (0 \times 2^4 = 0)
Now we sum these values:
- (0 + 0 + 4 + 8 + 0 = 12)
The sum yields 13.
To visualize it better, consider how each position contributes to the total value:
- The digit 1 in the (2^3) position (the fourth digit from the right) contributes (8).
- The digit 1 in the (2^2) position contributes (4).
- The digit 0 in the (2^4) position contributes nothing.
- The rightmost digits contribute a total of (0 + 2 = 2).
Adding these contributions together gives (8 + 4 + 0 + 1 = 13).
In conclusion, the binary number 01101 equals 13 in decimal, making option B the correct answer. Understanding how to convert binary to decimal is crucial, especially in fields like computer science and electronics, where binary representation is fundamental.